Work

Local Constant Approximation for Dominating Set on Graphs Excluding Large Minors

Year: 2025

Type: conference-paper

Abstract: We show that graphs excluding K2,t as a minor admit a f(t)-round 50-approximation deterministic distributed algorithm for Minimum Dominating Set. The result extends to Minimum Vertex Cover. Though fast and approximate distributed algorithms for such problems were already known for H-minor-free graphs, all of them have an approximation ratio depending on the size of H. To the best of our knowledge, this is the first example of a large non-trivial excluded minor leading to fast and constant-approximation distributed algorithms, where the ratio is independent of the size of H. A new key ingredient in the analysis of these distributed algorithms is the use of asymptotic dimension.

Source: ACM Symposium on Principles of Distributed Computing (PODC)

DOI: 10.1145/3732772.3733531

Authors: Marthe Bonamy, Cyril Gavoille, Timothe Picavet, Alexandra Wesolek

Institutions: Centre National de la Recherche Scientifique, Université de Bordeaux, Laboratoire Bordelais de Recherche en Informatique, Technische Universität Berlin

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche, Berlin Mathematics Research Center MATH+